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## 2013-2014 Academic Year Colloquium Schedule

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### September 5, 2013

 Title: Planning for Graduate Study in Mathematics and Computer Science Speaker: David A. Reimann Professor Mathematics and Computer Science Albion College Albion, Michigan Abstract: A degree in mathematics or computer science is excellent preparation for graduate school in areas such as mathematics, statistics, computer science, engineering, finance, and law. Come learn about graduate school and options you will have to further your education after graduation. Location: Palenske 227 Time: 3:30 Citation Click for BibTeX citation

### September 12, 2013

 Title: Symmetries on Spheres Speaker: David A. Reimann Professor Mathematics and Computer Science Albion College Albion, Michigan Abstract: Symmetry is an important for many academic disciplines. Objects that are symmetric are often seen as possessing an aesthetic quality. In this talk, we will consider the types of symmetry patterns that can be placed on a sphere and mathematically demonstrate the number of these patterns. We will also look at how these symmetries can be mapped onto general three-dimensional objects. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### September 26, 2013

 Title: Between the Folds, a film by Vanessa Gould Speaker: Abstract: Green Fuse Films' award-winning documentary Between the Folds chronicles the stories of ten fine artists and intrepid theoretical scientists who have abandoned careers and scoffed at hard-earned graduate degrees—all to forge unconventional lives as modern-day paperfolders. As they converge on the unlikely medium of origami, these artists and scientists reinterpret the world in paper, and bring forth a bold mix of sensibilities towards art, expressiveness, creativity and meaning. And, together these offbeat and provocative minds demonstrate the innumerable ways that art and science come to bear as we struggle to understand and honor the world around us—as artists, scientists, creators, collaborators, preservers, and simply curious beings. "Luminously photographed", with a "haunting" original score featuring the Budapest Symphony Orchestra, the film paints an arresting portrait of the mysterious creative threads that bind us all–fusing science and sculpture, form and function, ancient and new. See www.greenfusefilms.com for more information. Location: Palenske 227 Time: 3:10 pm Citation Click for BibTeX citation

### October 3, 2013

 Title: What is the Point of Algebraic Geometry? A Variety of Examples Speaker: David C. Murphy Associate Professor Department of Mathematics and Computer Science Hillsdale College Hillsdale, Michigan Abstract: Algebraic geometry has been at the center of much of mathematics for hundreds of years. Its applications range from number theory to modern physics. Yet, it begins quite humbly with the study of conic sections: circles, ellipses, hyperbolas, and parabolas. What is algebraic geometry and how did it grow beyond the scope of these familiar curves to become one of the most important branches of mathematics today? In this talk, which will not be able to completely answer these questions, we will focus on its growth from the study of conic sections to the exploration of algebraic varieties. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### October 10, 2013

 Title: Mathematics and Fiber Arts: Some Intersections Speaker: Norma Taber 2013 Distinguished Alumni Award recipient Maryland Abstract: Color, texture, pattern - there's more than first meets the eye in my crocheting. Come for a hands-on experience and new insights into finding mathematics in unlikely objects and expressing math concepts in artful ways. Invite your knitting and crocheting friends, bring someone who claims "I can't do math," attend with a classmate who thinks math is too abstract to be interesting, bring along that education major or art student. Build a bridge between math and their world: enjoy this event together. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### October 24, 2013

 Title: Building an Actuarial Program - an exciting, interdisciplinary adventure! Speaker: Dr Albert Cohen Assistant Program Director, Actuarial Science Mathematics; Statistics and Probability Michigan State University East Lansing, Michigan Abstract: Since the early 2000's, MSU has offered students the opportunity to prepare for their career as an actuary as aprt of their academic training. In 2011, the Bachelor of Science in Actuarial Science was introduced as the newest major on campus. The program has developed into a highly prized major among students on campus, and we continue to expand as we seek to a world leader in actuarial education and research. In this talk, we will talk about the development of our program and how Albion students and faculty can develop one as well! All questions are encouraged during the session. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### October 31, 2013

 Title: EY - Intro to Data Analytics: Using Analytics to Build a Better Working World Speaker: Aaron Croad, '12 and Dennis O'Dowd, '13 Staff - Advisory Services Advanced Analytics Ernst & Young Detroit, MI Abstract: We live in an era where there has never been greater access to information. Being able to sift through and analyze this information to understand what is "noise" and what can actually lead to valuable insights has become a highly demanded commodity. In turn, so to have Data Analysts. For profit-seeking companies, the realization of business objectives through reporting of data to analyze trends, creating predictive models for forecasting and optimizing business processes for enhanced performance has become pivotal for sustainable success. In this talk, we will provide an introduction to data analytics and we will review how our employer, EY, uses data analytics to build a better working world. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### November 7, 2013

 Title: Ford Circles, Euclidean Rings, and Graph Coloring Speaker: Lon Mitchell Associate Editor Mathematical Reviews American Mathematical Society Ann Arbor, MI Abstract: A research problem concerning the Colin de Verdiere number of a graph recently led me on a journey that provides a great example of the interconnected nature of mathematics. We'll take a relaxing cruise through some of the topics involved, including ideas from Analysis, Algebra, Geometry, and Graph Theory, see how they all fit together, and talk about some of the mysteries that remain. Only knowledge of basic arithmetic is needed. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### November 14, 2013

 Title: Serious Game Design - Using Games To Make The World A Better Place Speaker: Culver Redd, '11 Game Designer and Software Engineer Communication Arts & Sciences (Recently graduated) Michigan State University (Recently graduated) TechSmith Corporation Lansing, MI Abstract: While games are ordinarily thought of as a means for entertainment and distraction, they are also inherently useful to accomplish all manner of other purposes. Among other things, games--both digital and physical--can be used to teach, modify behaviors, influence opinions, and improve physical and mental health. I will share some of the major heuristics that are useful in designing games for "serious" purposes, as well more general knowledge of game design and the game industry. Additionally, I will share my experiences as a graduate student in the serious game design MA program at Michigan State University. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### November 21, 2013

 Title: Adjusting Child Support Payments in Michigan Speaker: Michael A. Jones Asscoiate Editor Mathematical Reviews Ann Arbor, MI Abstract: Michigan uses an unusual formula in the calculation of child support payments. For divorced parents in Michigan, the base monetary support each parent is expected to contribute to raising their child is adjusted according to the number of (over)nights spent with the parents. Curiously, this adjustment is based on a rational polynomial function parameterized by $k$ that describes the amount of money that $A$ must pay $B$, where $B$ must pay $A$ if the result is negative. In the 2004 Michigan Child Support Formula Manual, $k = 2$, meaning the polynomials are quadratic; while $k=3$ (for cubic polynomials) in both the 2008 and 2013 editions. In this talk, we will brainstorm and collaborate in using calculus to examine this function, explain the effect of changing $k$, and point out an alternative form that stretches and translates a simpler function. This talk is based on joint work with Jennifer Wilson (New School University, New York). Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### December 5, 2013

 Title: Student Speakers Speaker: Mathematics Majors Mathematics and Computer Science Albion College Albion, Michigan Abstract: "Discount and Turnover in Closed-End Funds" Sarah Erdman, '14 "Wheel theory: How to divide by zero" Rebecca Guntz, '14 "Michaelis-Menten Derivation and Application" Alex Schumaker, '14 "Predicting Extreme Events: Critical Ruptures and Applications to Common Complex Situations." Robin Todd, '14 "A Markov Chain Analysis of the National Football League's Overtime Rule" Laura VerHulst, '14 Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### January 30, 2014

 Title: Careers in Mathematics and Computer Science Speaker: David A. Reimann Associate Professor Mathematics and Computer Science Albion College Albion, MI, USA Abstract: A degree in mathematics or computer science is excellent preparation for employment in areas such as teaching, actuarial science, software development, engineering, and finance. Come learn about career opportunities awaiting you after graduation. Slides from the talk are available at http://zeta.albion.edu/~dreimann/talks/careers/careers.html. Location: Palenske 227 Time: 3:10 PM Citation Click for BibTeX citation

### February 6, 2014

 Title: From Waste to Biogas - Insights through Mathematical Modeling Speaker: Marion Weedermann Chair, Director of Joint Engineering Program with IIT Department of Mathematics Dominican University River Forest, IL Abstract: Anaerobic digestion is a biochemical process in which organic matter is broken down to biogas and various byproducts in an oxygen-free environment. When used in waste treatment facilities, the biogas is captured before it escapes into the atmosphere. It can then be used as renewable energy either by combusting the gas to produce electrical energy or by extracting the methane and using it as a natural gas fuel. In industrial applications anaerobic digestion appears to be difficult to control and reactors often experience break-down resulting in little or no biogas production. In this talk we describe a model for anaerobic digestion and illustrate how qualitative and numerical analysis give guidelines for how to control the system to (1) stabilize and (2) optimize biogas production. At the same time the model explains various possible pitfalls in industrial installations. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### February 13, 2014

 Title: Bernoulli Numbers and Polynomials Speaker: David Gaebler Assistant Professor Mathematics Hillsdale College Hillsdale, MI Abstract: Question: What do sums of powers have to do with approximations of factorials? Answer: Integration by parts. No, really! In this talk we will see how a clever use of standard calculus techniques leads to the Euler-Maclaurin formula, a powerful way of connecting sums to integrals, and how this formula solves several classic problems. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### February 20, 2014

 Title: The Mathematics of Blackjack Speaker: Mark Bollman Professor and Chair Mathematics and Computer Science Department Albion College Albion, MI Abstract: Blackjack, or 21, is among the most popular casino table games. Since unlike most other games of chance, successive hands of blackjack are not independent, the mathematics behind blackjack is at once more complicated and more interesting than for games like craps or roulette, and there can be times during play when the gambler has an edge over the casino. This talk will briefly review the rules of the game and then describe some of the calculations--both theoretical and experimental--that led to blackjack basic strategy and the advantages derived from card counting. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### February 27, 2014

 Title: The Colley Matrix as an Extension of the Borda Count Speaker: Michael A. Jones Associate Editor Mathematical Reviews American Mathematical Society Ann Arbor, MI Abstract: The Colley method was one of the six computer-based ranking methods used to determine the top ten NCAA football teams to play in bowl games as part of the Bowl Championship Series. The Colley method uses a matrix to rank order the teams based on win-loss data; the method accounts for strength of schedule. The Borda Count is a well-known voting procedure with a long history. By viewing voters' preferences as win-loss data, the Colley method can be used to determine the winner of an election. Surprisingly, the Colley ranking agrees with the ranking from the Borda count. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### March 3, 2014

 Title: What exactly is half a derivative anyway? Speaker: William R. Green, '05 Assistant Professor Department of Mathematics Rose-Hulman Institute of Technology Terre Haute, Indiana Abstract: The theory of differentiation is well-known to any student who has taken calculus. However, to make sense of a non-integer order derivative takes considerably more work. Tools are needed from complex analysis, harmonic analysis and linear algebra to understand a half derivative. In this talk, we will begin by investigating what it means to take the square root of a matrix, and viewing a derivative as a "really large matrix" we can begin to make sense of a half derivative. With these simple tools, we can make sense of even crazier objects such as derivatives of imaginary order! Location: Palenske 223 Time: 1:00 PM Citation Click for BibTeX citation

### March 6, 2014

 Title: Partial Geometries and Strongly Regular Graphs: Connections and Questions Speaker: Ellen Kamischke Teaching Assistant Mathematics Michigan Technological University Houghton, Michigan Abstract: Partial geometries were first described in 1963 by R. C. Bose. They are finite point line geometries specified by three parameters that are defined by a set of four basic axioms. Each partial geometry has a strongly regular point graph. While some very simple shapes can be understood as partial geometries, the number of proper ones is actually limited. In this talk we will define both the geometries and the graphs and explore some connections between them. We will also look at how we can use a group of automorphisms acting on the geometry to classify it as one of three types. Finally we will see how this work enables us to generate a list of parameters for potential partial geometries and how we are beginning to investigate these possibilities. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### April 3, 2014

 Title: Fractals, p-adics, and a problem of Erdős Speaker: William Abram Assistant Professor Mathematics Hillsdale College Hillsdale, Michigan Abstract: Erdős asked: when does the base 3 expansion of a power of 2 omit the digit 2? His conjectured answer is that this only happens for 1, 4, and 256, but this conjecture is still open, and has proven to be very elusive. There underlies a deep relationship between the primes 2 and 3. Our attempt to understand this relationship has led to interesting connections among symbolic dynamical systems, graph theory, p-adic analysis, number theory, and fractal geometry. Despite the awesome variety of mathematics involved, linear algebra should be sufficient background knowledge for this talk. I report on joint work with Jeff Lagarias of the University of Michigan and Artem Bolshakov of the University of Texas at Dallas. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### April 10, 2014

 Title: Stripes, Squares, & Oscillons: An Introduction to Mathematical Modeling and Pattern Formation Speaker: Catherine Crawford Associate Professor Mathematics Elmhurst College Elmhurst, IL Abstract: Patterns appear everywhere in the world around us from zebra stripes, to hexagonal honeycombs, to spiral arrangements of sunflower seeds, to the periodic ups and downs of a population size due to seasonal migration. Similar patterns also arise in experiments done in many disciplines, such as physics, chemistry, and biology. One goal in studying pattern formation is to understand why and how these patterns are created. Another goal is to determine whether similar patterns from vastly different systems can be described and understood through similar mathematical model equations. This talk will describe how a pattern can be represented mathematically and how basic knowledge of functions and derivatives can help determine when and where the patterns will exist. Analytical and numerical results will be compared with experimental observations. Finally, the connection between the underlying pattern and the observation of a single, isolated pulse, called an oscillon, will be described. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### April 17, 2014

 Title: Operations Research/Advanced Analytics: Opportunities and Methods in Applied Math Speaker: Andrew M. Ross Associate Professor Mathematics Eastern Michigan University Ypsilanti, MI Abstract: Operations Research is an area of applied math that deals with analyzing and optimizing many different systems: industrial, nonprofit, government, healthcare, etc. It operates at the intersection of math, engineering, statistics, computer science, and business. We will talk about common focus areas like minimizing waiting times for important public services, and scheduling staff in an optimal way. The methods are incredibly powerful--optimization decisions can often involve hundreds of thousands of variables, and sometimes millions or billions. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### May 1, 2014

 Title: Integrating Hands-On Exploration to Build Student Understanding: Pedagogically Based Reasoning behind Including Hands-On Manipulatives in Secondary Math Classrooms Speaker: Cara Delaney, 14 Senior Mathematics Major Albion College Albion, Michigan Abstract: Teachers have to make decisions everyday- about what material to cover, what activities to plan, how those activities will be assessed- and good teachers make pedagogically based decisions. In math classrooms, abstract content can, at times, be seemingly inaccessible to some students. By including hands-on manipulatives into the classroom, students can kinetically explore content to help bridge their understanding. These manipulatives can be incorporated in a variety of ways depending on the intended purpose. Using an example of a movable integral model, some of those possibilities for activities will be shown and explained. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### May 1, 2014

 Title: Modeling Coral Reef Dynamics Speaker: Jennifer Polinski, 14 Senior Mathematics Major Albion College Albion, Michigan Abstract: Many models of coral reef dynamics created before 2012 fell into one of two categories: they were either conceptual models not intended to give realistic descriptions of natural reef dynamics or were fully specified in that they assumed particular parameters. Both types of models tell what is possible, but do not necessarily tell what occurs in nature. My presentation will be analyzing the mathematical model developed in the paper "Data-driven models for regional coral-reef dynamics," by Kamila Zychaluk, John F. Bruno, Damian Clancy, Tim R. McClanahan, and Matthew Spencer (Ecology Letters, 15:151-158). This model differed from past models in that it was only partially specified, allowing greater flexibility. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation

### May 1, 2014

 Title: Wheels: How to Divide by Zero Speaker: Brian Wu, `14 Senior Mathematics Major Albion College Albion, Michigan Abstract: As a young student, we initially learned that we could not take the square root of a negative number. Eventually, we learned about the set of complex numbers, which was invented in order to calculate all of the roots of any polynomial, including those involving square roots of negative numbers. Additionally, we learned that parallel lines never intersect. Upon looking at them from a new perspective, we learned that in projective geometry, parallel lines intersect at a point "at infinity." Currently, we are told that division by zero is a forbidden mathematical operation due to the lack of a multiplicative inverse. Alternately, there is no solution to the equation $0x = 1$. However, mathematicians recently defined $\perp$ and $\infty$, consistent with previous mathematics, representing the two cases that arise when attempting to divide by zero. These two new elements are placed into a field, yielding a special structure called a wheel. However, division by zero is not entirely without consequences. This talk will review the familiar algebraic structures, including rings and fields, and then proceed onto wheels and how incorporating these two new elements change the properties of polynomials. Location: Palenske 227 Time: 3:30 PM Citation Click for BibTeX citation